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The field of computational science continues to make significant strides, particularly in artificial intelligence (AI), mathematical modeling, and optimization techniques. These innovations are not only reshaping industries such as drug discovery, engineering design, and hardware optimization but are also providing crucial tools for tackling complex scientific problems. The growing intersection of AI, machine learning, and traditional computational methods underscores the importance of developing novel algorithms and simulation environments for enhanced efficiency and accuracy [1].

This special issue brings together cutting-edge research from the “Mathematical Modeling and Problem Solving” workshop, held at the 30th International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA’24). Following the success of PDPTA'23 [2], this year’s PDPTA'24 once again attracted outstanding papers on the themes of mathematical modeling and problem-solving, highlighting the growing interest in this area. Nine papers have been carefully selected, showcasing a broad range of topics that span from natural language processing and AI-driven generation methods to system optimization and high-performance computing applications.

Four of these papers delve into AI-driven methods and recommendation systems, highlighting the potential of natural language processing and machine learning. Sakano et al. present NPGPT [3], an innovative approach that uses GPT-based chemical language models for the generation of natural product-like compounds, advancing the discovery process in the chemical sciences. Koiso et al. propose a method to acquire training data for early-modern Japanese-printed character recognition, offering an effective approach to historical text analysis [4]. Takata et al. demonstrate a similar music recommendation system using the Spotify API, which leverages song attributes to enhance user music discovery [5]. These papers illustrate how AI is being applied to diverse areas, from chemical design to cultural heritage preservation and entertainment.

Another two papers focus on computational hardware systems, demonstrating advancements in simulation environments and hardware sharing for performance optimization. Kawai et al. introduce a simulation environment for Reconfigurable Virtual Accelerators (ReVA), utilizing the Vivado Simulator to enhance computational efficiency [6]. Tanaka et al. evaluate the SHAVER system, which shares vector registers with an accelerator to optimize hardware performance [7]. Together, these papers underscore the importance of reconfigurable computing systems and hardware resource management in boosting the efficiency of modern computational tasks.

Three papers in this issue address optimization algorithms, particularly in the realm of evolutionary computing and complex problem-solving. Zhong et al. propose a Competitive Differential Evolution (CDE) algorithm with knowledge inheritance, designed to optimize the design of single-objective human-powered aircraft [8]. This method showcases the utility of evolutionary techniques in engineering design. Zhong et al. introduce a Hyper-heuristic Differential Evolution (HHDE) algorithm, which includes a novel boundary repair technique for solving complex optimization problems, highlighting the robustness of hyper-heuristic approaches [9]. Zhang et al. present a Vision Transformer-based approach combined with the Actor-Critic method to explore meta-loss landscapes, offering new insights into neural network training dynamics [10]. These works push the boundaries of what is achievable with advanced optimization algorithms in both theoretical and applied settings.

Finally, the last paper in this collection focuses on a high-speed numerical method for condition number computation. Chiyonobu et al. introduce a high-speed computation method for calculating condition numbers in the Range Restricted General Minimum Residual (RR-GMRES) method, improving the efficiency of solving large-scale linear systems [11]—a crucial step in fields requiring high-performance computing and numerical analysis.

In summary, this special issue provides a snapshot of the ongoing developments in AI, mathematical modeling, and system optimization. Each paper contributes novel approaches and practical solutions that further our understanding and ability to solve complex scientific and engineering challenges. The contributions presented here lay the foundation for future advancements in computational science, enhancing both theoretical exploration and practical applications across multiple disciplines.